Spectral information criterion for automatic elbow detection

We introduce a generalized information criterion that contains other well-known criteria, such as Bayesian Criterion (BIC) and Akaike (AIC), special cases. Furthermore, the proposed spectral (SIC) is also more general than e.g., since knowledge of likelihood function not strictly required. SIC extracts geometric features error curve and, consequence, it can be considered an automatic elbow detector. provides subset all possible models, with cardinality often much smaller total number models. The elements this are elbows curve. A practical rule for selecting unique model within sets suggested well. Theoretical invariance properties analyzed. Moreover, we test in ideal scenarios where always optimal expected results. several numerical experiments: some involving synthetic data, two experiments real datasets. They real-world applications clustering, variable selection, or polynomial order to name few. results show benefits scheme. Matlab code related provided. Possible future research lines finally discussed.